Analysis of a multi-axial quantum informed ferroelectric continuum model: Part 1—uncertainty quantification

Abstract

The uncertainty of phenomenological parameters governing fourth- and sixth-order Landau energy functions and electrostrictive coupling of ferroelectric single crystals is analyzed for lead titanate. Bayesian statistics are used to quantify model parameter uncertainty associated with approximating lattice strain and full-field electron density from density functional theory calculations as a homogenized, electromechanical continuum. The continuum model parameter uncertainty is propagated through the model to obtain prediction and credible intervals when estimating the non-convex energy surface and electrostrictive stresses for lead titanate. The results illustrate the important differences in fourth- and sixth-order Landau energy functions that influence estimations of the crystal phase. In addition, Bayesian statistics provides important insights into varying degrees of uncertainty along different thermodynamic paths associated with polarization rotation versus polarization changes along its spontaneous direction. Methods to reduce this uncertainty via decoupling electromechanical relations are demonstrated. The results provide critical insight into the development of self-consistent models that utilize density functional theory for large-scale continuum model simulations. Furthermore, the results are complementary to Part 2, in which we develop and apply new concepts in model parameter global sensitivity to accelerate uncertainty quantification of correlated parameters using higher order energy functions for a broad range of ferroic materials.